Quick Question

A child is lying on her back. The tension in the muscles of her neck is 55N as she raises her head to look past her toes and out the motel window. Ten minutes later she is screaming and sliding feet first down a water slide at a constant speed of 5.7 m/s in a horizontal curve of radius 2.40 m. She raises her head to look forward past her toes; find the tension in the muscles in her neck.

First case:
The tension provides the necessary force to balance the weight of the lifted part of her body (for simplicity, let's call that "the head" in the following)
Use this to determine the head's mass.
For the second case:
Note that when her head does NOT touch the slide, only the tension in her neck provides the force necessary for the centripetal acceleration the head experiences.

If you wouldn't mind helping me again, I have another question that I'm stumped on.

A plumb bob does not hang exactly along a line directed to the center of the Earth because of the Earth's rotation. How much does the plumb bob deviate from a radial line @ 35 degrees north latitude? Assume the Earth is spherical.

I combined the x and y components of the bob to get (4*pi²*r)/(T²g) = tan(x). What numbers would I use for r and T? I think I could use 24 hrs. for T, but r wouldn't be the Earth's radius.